A radioactive nucleus ${ }_Z^{A}X$ undergoes spontaneous decay in the sequence ${ }_Z^{A}X{\to }_{z-1}B{\to }_{z-3}C{\to }_{z-2}D,$ where Z is the atomic number of an element X. The possible decay particles in the sequence are

$X_z^A\to \underset{z-1}{B}\to$ atomic number decrease by 1 unit the emitted particle ${\beta }^{+}$        

$\underset{z-1}{B}\to \underset{z-3}{C}\to$ atomic number decrease by 2 unit the emitted particle “$\alpha$”

$\underset{z-3}{C}\to \underset{z-2}{D}\to$ atomic number increase by 1 unit the emitted particle ${\beta }^{-}$